is the CFT Hamiltonian. (Here and below we consider 2d CFT on a cylinder. Because of standard factorization into left and right-moving sectors we restrict the discussion to one sector only.) Interest in integrable structure of 2d CFT stress-energy sector has been reignited recently in the context of Eigenstate Thermalization Hypothesis (ETH) [1]}. Following original works [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]} it has been conjectured and confirmed in [11]} that 2d CFTs exhibit generalized ETH with the local equilibrium being described by qKdV Generalized Gibbs Ensemble (GGE). Schematically the role of qKdV charges is as follows. The CFT Hamiltonian (REF ) is highly degenerate
with all CFT descendant states of the form
\(|E\rangle =L_{-m_1} \dots L_{-m_k} |\Delta \rangle ,\qquad \sum _{i=1}^k m_i=m\) 
